#### Presentation Title

Characterizing Parallelograms with Sides and Diagonals Having Integer Lengths

#### Presentation Type

Oral Presentation

#### School

School of Sciences and Social Sciences

#### Discipline

Mathematics

#### Mentor

Vincent Ferlini

#### Date & Time

April 9th at 10:15 AM - 11:15 AM

#### Location

David F. Putnam Science Center, Room 102

#### Abstract

A perfect parallelogram is defined as a parallelogram whose sides and diagonals are positive integers. We first look at three separate cases one of which is a general parallelogram where the sides and diagonals satisfy the parallelogram equation. The second case is a perfect rational parallelogram where the sides and diagonals are positive rational numbers. Then the third case is a perfect parallelogram. The use of up to scaling on each of the above parallelograms is used to make the observation that all perfect parallelograms have a parameterization. We then look at the special case of each of the above in which a perfect rectangle is obtained.

Characterizing Parallelograms with Sides and Diagonals Having Integer Lengths

David F. Putnam Science Center, Room 102

A perfect parallelogram is defined as a parallelogram whose sides and diagonals are positive integers. We first look at three separate cases one of which is a general parallelogram where the sides and diagonals satisfy the parallelogram equation. The second case is a perfect rational parallelogram where the sides and diagonals are positive rational numbers. Then the third case is a perfect parallelogram. The use of up to scaling on each of the above parallelograms is used to make the observation that all perfect parallelograms have a parameterization. We then look at the special case of each of the above in which a perfect rectangle is obtained.